Find All Trig Functions of Gamma Given cot(gamma)=4/3

In summary, the value of gamma cannot be determined based on the given information and additional information is needed to calculate it. Cotangent is the reciprocal of tangent and the relationship between cot(gamma) and the other trigonometric functions can be determined by using the Pythagorean theorem. The values of sine, cosine, and tangent of gamma can be found by first finding the value of gamma and then using the ratios of the sides of a right triangle. A calculator can be used to find the values of the trigonometric functions, but make sure to use the correct mode and input the value of gamma correctly. The accuracy of the calculated values can be verified by using the inverse trigonometric functions.
  • #1
dora1
1
0
Given cot(gamma)=4/3 find all possible values of the five remaining trigonometric functions of γ.

Could somebody help me here?
Thanks
 
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  • #2
Let's make a diagram.

\begin{tikzpicture}
\draw (0,0) node[anchor=north]{$A$}
-- (4,0) node[anchor=north]{$C$}
-- (4,4) node[anchor=south]{$B$}
-- cycle;
\end{tikzpicture}

Using the given information and Pythagoras:

$$\overline{AC}=4\quad\overline{BC}=3\quad\overline{AB}=5$$

Now, can you determine the five remaining trigonometric ratios?
 

FAQ: Find All Trig Functions of Gamma Given cot(gamma)=4/3

1. What is the value of gamma in this equation?

The value of gamma cannot be determined solely based on the given information. Additional information is needed to calculate the exact value of gamma.

2. What is the relationship between cot(gamma) and the other trigonometric functions?

Cotangent is the reciprocal of tangent, and tangent is the ratio of the opposite side to the adjacent side in a right triangle. Therefore, the relationship between cot(gamma) and the other trigonometric functions can be determined by using the Pythagorean theorem.

3. How do I find the values of sine, cosine, and tangent of gamma?

The values of sine, cosine, and tangent of gamma can be found by first finding the value of gamma using additional information and then using the ratios of the sides of a right triangle to calculate the values of the trigonometric functions.

4. Can I use a calculator to find the values of the trigonometric functions?

Yes, you can use a calculator to find the values of the trigonometric functions. Make sure to use the correct mode (degrees or radians) and input the value of gamma correctly.

5. How can I verify that my calculated values of the trigonometric functions are correct?

You can verify your calculated values by using the inverse trigonometric functions. For example, if you have calculated the value of sine of gamma, you can use the inverse sine function to check if the calculated value is correct.

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